Cardiorespiratory Dynamics as a Non-Autonomous System of Coupled Oscillators with Time-Varying Frequency Modulation

We model the cardiorespiratory interaction as arising within a collection of coupled, non-autonomous, nonlinear oscillators with explicitly time-dependent frequency modulation. The resulting system is analysed in terms of phase tracking and stability using finite-time Lyapunov exponents. We show that synchronisation emerges from the interplay between coupling strength, intrinsic frequency mismatch, and modulation amplitude, giving rise to regimes of stable entrainment, intermittent synchronisation, and desynchronised dynamics. The transitions between these regimes are governed by the system's ability to track time-dependent attractors rather than by fixed phase-locking conditions. Numerical simulations, together with physiological recordings, demonstrate that time-varying modulation and interaction structure are both essential to reproduce observed cardiorespiratory behaviour. In particular, the data indicate that coupling is not stationary but evolves over time, contributing significantly to the observed variability in synchronisation patterns. These results suggest that the cardiorespiratory interaction is more naturally interpreted as an emergent property of a non-autonomous dynamical system with evolving interaction geometry and moving attractors, rather than as a stationary coupling process between autonomous oscillators.